Determination of an item of position information relating to a position of a magnetic field transducer relative to a position sensor

ABSTRACT

An apparatus for determining an item of position information relating to a position of a magnetic field transducer relative to a position sensor. The position sensor is designed to generate at least one periodic measurement signal when the magnetic field transducer moves relative to the position sensor. A processing unit of the apparatus is designed to determine the position information based on a respective measurement signal value of a respective periodic measurement signal using a calibration function assigned to the respective periodic measurement signal. The assigned calibration function represents the respective periodic measurement signal using a Fourier series having a respective plurality of Fourier coefficients which differ from zero and are of an order greater than zero. The processing unit is designed to at least approximately solve the assigned calibration function for the respective measurement signal value in order to determine the position information.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to German Patent Application No.102019218702.1 filed on Dec. 2, 2019, the content of which isincorporated by reference herein in its entirety.

DESCRIPTION

The present disclosure deals with apparatuses and methods fordetermining an item of position information relating to a position of amagnetic field transducer relative to a position sensor, wherein theposition sensor is designed to generate at least one periodicmeasurement signal when the magnetic field transducer moves relative tothe position sensor. The present disclosure also relates to a positionsensor.

BACKGROUND

Position sensors are used to measure a position or a movement of amagnetic field transducer relative to the position sensor. Examples ofposition sensors have magnetic field sensors, such as xMR sensors orHall sensors, wherein xMR denotes different magnetoresistive effectssuch as AMR (anisotropic magnetoresistance), GMR (GMR=giantmagnetoresistance) and TMR (TMR=tunnel magnetoresistance). Theseposition sensors provide a measurement signal which is proportional toan applied magnetic field. The magnetic field transducer may have one ormore pole pairs, for example, with the result that the position sensorgenerates an oscillation signal, which fluctuates around a mean value,in the event of a relative movement between the position sensor and themagnetic field transducer.

Such position sensors are used, for example, in sensor systems whichcapture an angular position of a rotating shaft. Examples of such sensorsystems are so-called “out-of-shaft” sensor systems in which theposition sensor is arranged outside the shaft, for example beside theshaft. In the case of so-called “end-of-shaft” or “integratedend-of-shaft” sensor systems, the position sensor can be arranged at theend of the shaft. In particular, “out-of-shaft” sensor systems can alsobe used when the axis of rotation is not accessible. In the case ofsensor systems for capturing an angular position, a magnetic fieldtransducer having one or a plurality of pole pairs may be arranged onthe axis of rotation, wherein the magnetic poles may be arrangedalternately in the direction of rotation, with the result that themagnetic field transducer generates a varying, for example a periodic,magnetic field during a rotation of the axis of rotation, which magneticfield is captured by the position sensor.

Magnetic synchros are currently used in such sensor systems as positionsensors. For this purpose, a specially shaped ring made of aparamagnetic material is fastened to the axis of rotation. The ringrotates inside an arrangement of two arrangements of coils. The firstarrangement of coils generates an alternating magnetic field, while thesecond arrangement of coils detects the alternating magnetic field.Magnetic coupling between the two arrangements of coils is modulated bythe angular position of the paramagnetic ring. In a similar manner tothe core of a transformer, the coupling changes depending on whethermore or less of the paramagnetic material of the ring is situatedbetween the two arrangements of coils. The rotor, or a part of thelatter, modulates the air gap between the exciting and the receivingcoils. It may therefore be necessary to precisely arrange the stator,for example the coils, and the rotor, for example the rotating shaft. Inaddition, special assembly parts, for example rings, sleeves, screws,are used to permanently fix the stator and rotor parts.

The properties imposed on position sensors for use in such sensorsystems generally usually lie in a high degree of robustness withrespect to stray fields and a high degree of accuracy of the measuredangle.

OVERVIEW

A concept for determining an item of position information relating to aposition of a magnetic field transducer relative to a position sensorwould is described herein, which concept makes it possible topermanently determine the position information as consistently aspossible and as precisely as possible and, at the same time, enables adesign of the position sensor which is as simple, space-saving andcost-effective as possible.

Examples of the prfesent disclosure provide an apparatus for determiningan item of position information relating to a position of a magneticfield transducer relative to a position sensor, wherein the positionsensor is designed to generate at least one periodic measurement signalwhen the magnetic field transducer moves relative to the positionsensor. The apparatus has a processing unit which is designed todetermine the position information on the basis of a respectivemeasurement signal value of a respective periodic measurement signalusing a calibration function assigned to the respective periodicmeasurement signal. In this case, the assigned calibration functionrepresents the respective periodic measurement signal using a Fourierseries having a respective plurality of Fourier coefficients whichdiffer from zero and are of an order greater than zero. Furthermore, theFourier coefficients are determined on the basis of a respectivemultiplicity of measurement signal values of the respective periodicmeasurement signal. The processing unit is designed to at leastapproximately solve the assigned calibration function for the respectivemeasurement signal value in order to determine the position information.

Examples of the present disclosure are based on the knowledge that theuse of a calibration function which represents the periodic measurementsignal using a Fourier series having a plurality of Fourier coefficientswhich differ from zero makes it possible to adapt the calibrationfunction in a particularly precise manner even when the position sensoris arranged with respect to the magnetic field transducer in such amanner that the periodic measurement signal has a particularlyasymmetrical shape. On account of the particularly accurate calibrationfunction, the disclosed apparatus allows the position information to bedetermined precisely even in the case of an inaccurate geometry of asensor arrangement. As a result, the position information can bedetermined accurately using a simple or cost-effective sensorarrangement. As a result of the fact that the Fourier coefficients aredetermined on the basis of a multiplicity of measurement signal valuesof the periodic measurement signal and as a result of the fact that theprocessing unit is designed to at least approximately solve the assignedcalibration function for the respective measurement signal value, thecalibration function can be newly determined during operation, on theone hand, and the position information can be determined, on the otherhand, on the basis of the measurement signal value of the periodicmeasurement signal and using the calibration function, even a newlydetermined calibration function. This makes it possible to permanentlyprecisely determine the position information even when an arrangement ofthe position sensor with respect to the magnetic field transducerchanges over time. In addition, a particular robustness of the positionsensor with respect to stray fields can thus be achieved.

Examples of the present disclosure provide a method for determining anitem of position information relating to a position of a magnetic fieldtransducer relative to a position sensor, wherein the position sensor isdesigned to generate at least one periodic measurement signal when themagnetic field transducer moves relative to the position sensor. Themethod comprises determining the position information on the basis of arespective measurement signal value of a respective periodic measurementsignal using a calibration function assigned to the respective periodicmeasurement signal, wherein the assigned calibration function representsthe respective periodic measurement signal using a Fourier series havinga respective plurality of Fourier coefficients which differ from zeroand are of an order greater than zero. The determination of the positioninformation comprises at least approximately solving the assignedcalibration function for the respective measurement signal value. Themethod also comprises determining the Fourier coefficients on the basisof a respective multiplicity of measurement signal values of therespective periodic measurement signal.

Examples of the present disclosure provide a position sensor, whereinthe position sensor has a measurement unit which is designed to generateat least one periodic measurement signal when a magnetic fieldtransducer moves relative to the position sensor, and wherein theposition sensor has the apparatus described herein for determining anitem of position information in order to determine the positioninformation on the basis of the at least one periodic measurementsignal.

Examples of the present disclosure provide a computer program having aprogram code for carrying out the method described herein when theprogram runs on a computer.

BRIEF DESCRIPTION OF THE DRAWINGS

Examples of the present disclosure are described below with reference tothe accompanying drawings, in which:

FIG. 1 shows a schematic illustration of an example of an apparatus fordetermining an item of position information,

FIG. 2A shows a schematic illustration of an example of an arrangementof a magnetic field transducer and a position sensor,

FIG. 2B shows a schematic illustration of an example of a magnetic fieldtransducer,

FIG. 3 shows a graph having an example of two periodic measurementsignals,

FIGS. 4A-C show graphs having an example of a periodic measurementsignal and one example of a Fourier series each,

FIG. 5 shows a graph having an example of two weighting functions,

FIG. 6A shows a graph having examples of a maximum error of an item ofposition information determined using a current solution on the basis ofan arrangement of the position sensor,

FIG. 6B shows a graph having examples of a maximum error of an item ofposition information determined using the disclosed apparatus on thebasis of an arrangement of the position sensor,

FIG. 7 shows a schematic illustration of an example of an arrangement ofa position sensor and a magnetic field transducer,

FIG. 8 shows a flowchart of an example of a method for determining anitem of position information,

FIG. 9 shows a flowchart of a further example of a method fordetermining an item of position information,

FIG. 10A shows a graph having an example of an error of an item ofposition information determined using a current solution,

FIG. 10B shows a graph having an example of an error of an item ofposition information determined using the disclosed apparatus.

DETAILED DESCRIPTION

Examples of the present disclosure are described in detail below usingthe accompanying drawings. It should be pointed out that identicalelements or elements having the same functionality can be provided withidentical or similar reference signs, wherein a repeated description ofelements which are provided with the same or a similar reference sign istypically omitted. Descriptions of elements having the same or similarreference signs can be interchanged with one another. Many details aredescribed in the following description in order to provide a moredetailed explanation of examples of the disclosure. However, it isobvious to experts that other examples can be implemented without thesespecific details. Features of the different examples described can becombined with one another unless features of a corresponding combinationexclude one another or such a combination is expressly excluded.

In examples, the position information relates to a rotational angle θ ofa magnetic field transducer 20 which has, for example, a magnetic ring21 arranged on a mounted shaft 22, for example a diametrically polarizedmagnetic ring. An example of such an arrangement is illustrated in FIG.2A. The magnetic ring 21 has a pole pair, wherein opposite poles in thepole pair are arranged alternately in the radial direction with respectto the magnetic ring 21. A position sensor 60 arranged beside themagnetic field transducer 20 is designed to capture a magnetic fieldgenerated by the magnetic field transducer 20 using a measurement unit,for example a magnetic field sensor, for example an xMR sensor or a Hallsensor mentioned at the outset. In FIG. 2A, the axis of rotation 24 isarranged along the z direction of a Cartesian coordinate system. Theposition sensor 60 can be designed to generate different measurementsignals on the basis of different spatial components of the magneticfield.

In examples, the position sensor 60 is designed to generate a firstmeasurement signal on the basis of a magnetic field component Ax in thex direction and to generate a second measurement signal on the basis ofa magnetic field component Ay in the y direction.

Further examples of the disclosure use an individual measurement signalor a plurality of different measurement signals.

In examples, the magnetic field transducer 20 generates a periodicallyfluctuating magnetic field in the event of a rotation of the magneticfield transducer 20 around an axis of rotation 24 at the position of theposition sensor 60, on the basis of which the position sensor 60generates the at least one periodic measurement signal. Examples of afirst periodic measurement signal 11A and a second periodic measurementsignal 11B are shown in FIG. 3. The periodic measurement signals areprovided, for example, as an analog signal or as a digital signal, forexample as ADC values (ADC=analog digital converter). In order to beable to infer a rotational angle θ, for example the positioninformation, from a measurement signal value of a periodic measurementsignal 11A; 11B provided by the position sensor 60, a calibrationfunction which is specific to the periodic measurement signal andrepresents the signal profile of the periodic measurement signal isused. The more accurately the calibration function reflects the periodicmeasurement signal, the more accurately the rotational angle can bedetermined on the basis of a measurement signal value.

In examples, a periodic measurement signal may have a sinusoidal profilewith respect to the rotational angle θ. In this case, a calibrationfunction of a measurement signal can be described or implemented using asine function. Such ideal sinusoidal signal profiles are shown in FIG. 3as dashed lines. In reality, the periodic measurement signals 11A; 11B,as shown in FIG. 3, may deviate from the ideal sinusoidal signalprofile, for example on account of mechanical inaccuracies or magneticinterference fields which can result in an asymmetrical signal profile,for example.

In examples, the position sensor 60 is arranged beside the magnetic ring21 in the radial direction, with the result that an air gap of thethickness 26 exists between the position sensor 60 and the magnetic ring21. For example, the position sensor 60 is ideally arranged in acentered manner in the axial direction (z direction in FIG. 2A) withrespect to the magnetic ring 21, but the position sensor 60 may also beshifted by a z offset 28 with respect to the centered arrangement.Furthermore, the position sensor 60 may also have an offset in the ydirection with respect to a central position with respect to the axis ofrotation 24.

So that the calibration function represents the periodic measurementsignal as accurately as possible in the case of deviations of theperiodic measurement signal from a sinusoidal profile, the calibrationfunction is represented using a Fourier series according to thedisclosure. FIGS. 4A-C show graphs which correspond to the graph shownin FIG. 3 and have examples of the first periodic measurement signal 11Aand of a representation of a Fourier series shown as a dashed line. InFIG. 4A, the Fourier series has a first-order Fourier coefficient ciwhich differs from zero. In FIGS. 4B and 4C, the Fourier series has thefirst-order and third-order Fourier coefficients c₁ and c₃ andfirst-order, second-order and third-order Fourier coefficients c₁, c₂and c₃ which differ from zero. As a result of the fact that thecalibration function represents the periodic measurement signal using aFourier series having a plurality of Fourier coefficients which differfrom zero and are of an order greater than zero, the calibrationfunction can approximate the periodic measurement signal particularlywell, as a result of which particularly accurate calibration can beachieved.

Solving the calibration function makes it possible to determine theposition information, for example the rotational angle θ, on the basisof a measurement signal value. The calibration function is approximatelysolved, for example, by evaluating the calibration function for anestimated value of the rotational angle, wherein the estimated value isvaried until a result of the evaluation of the calibration function iswithin an error tolerance around the measured measurement signal value.On account of the periodicity of the calibration function, this methodcan result in at least two different solutions of the calibrationfunction. Using a previous item of position information, for example thelast known previously determined angle, as the starting value foriteratively solving the calibration function makes it possible toensure, assuming a small change in the position information, that thesolving operation leads to the correct solution of the differentsolutions of the calibration function, that is to say the iterativelyadapted estimated value is at least in the vicinity of the actual value.On account of this type of solution using the previous positioninformation, the disclosed method also functions with only one periodicmeasurement signal in contrast to determining the rotational angle usingan arc tangent function.

The accuracy of the adapted estimated value may be lower in the regionof minima and maxima of the calibration function than in regions inwhich the calibration function has a greater gradient. In order todetermine the position information as accurately as possible, a weightedmean value of a plurality of estimated values can therefore bedetermined. In examples, the first periodic measurement signal and thesecond periodic measurement signal are phase-shifted through 90°, withthe result that the gradient of the first calibration function isgreatest at the positions at which the gradient of the secondcalibration function disappears. Accordingly, a contribution of arespective estimated value can be weighted according to the gradient ofthe respective calibration function at the position determined by therespective estimated value in order to determine the positioninformation in a very accurate manner.

FIG. 1 shows a schematic illustration of an example of an apparatus 10for determining an item of position information 19 relating to aposition of a magnetic field transducer 20 relative to a position sensor60, wherein the position sensor 60 is designed to generate at least oneperiodic measurement signal when the magnetic field transducer 20 movesrelative to the position sensor 60. The magnetic field transducer 20 andthe position sensor 60 are illustrated using dashed lines in FIG. 1since they are not part of the apparatus 10 in examples. In particular,the arrangement of the magnetic field transducer 20 and of the positionsensor 60 relative to the apparatus 10 should be understood by way ofexample. For example, the apparatus 10 and the position sensor 60 may bepart of the respective other or may each independent apparatuses. Theapparatus 10 has a processing unit 15. The processing unit 15 iscommunicatively connected to the position sensor 60, for example usingan electrical conductor or wirelessly, in order to receive the at leastone periodic measurement signal from the position sensor 60. Theprocessing unit 15 is designed to determine the position information 19on the basis of a respective measurement signal value of a respectiveperiodic measurement signal using a calibration function assigned to therespective periodic measurement signal. The assigned calibrationfunction represents the respective periodic measurement signal using aFourier serious having a respective plurality of Fourier coefficientswhich differ from zero and are of an order greater than zero, whereinthe Fourier coefficients are determined on the basis of a respectivemultiplicity of measurement signal values of the respective periodicmeasurement signal. For example, an assigned calibration functionrespectively represents a periodic measurement signal, wherein theFourier coefficients are determined specifically for one calibrationfunction in each case. Furthermore, the processing unit 15 is designedto at least approximately solve the assigned calibration function forthe respective measurement signal value in order to determine theposition information 19. That is to say, the position sensor 60 isdesigned to generate a first periodic measurement signal 11A when themagnetic field transducer 20 moves relative to the position sensor 60,and the processing unit 15 is designed to determine the positioninformation 19 on the basis of a first measurement signal value, whichrepresents a value of the first periodic measurement signal 11A, using afirst calibration function 13A assigned to the first periodicmeasurement signal 11A. In this case, the first assigned calibrationfunction 13A represents the first periodic measurement signal 11A usinga Fourier series having a first plurality of Fourier coefficients whichdiffer from zero and are of an order greater than zero, wherein theFourier coefficients are determined on the basis of a first multiplicityof measurement signal values of the first periodic measurement signal11A. In this case, the processing unit 15 is designed to at leastapproximately solve the assigned calibration function for the firstmeasurement signal value in order to determine the position information19. The option also exists of the position sensor 60 being designed togenerate a further periodic measurement signal 11B when the magneticfield transducer 20 moves relative to the position sensor 60. Inexamples, the processing unit 15 is designed to accordingly determinethe position information 19 on the basis of a further measurement signalvalue, which represents a value of the further measurement signal, usinga further calibration function assigned to the further periodicmeasurement signal.

In examples, the at least one periodic measurement signal comprises afirst periodic measurement signal 11A and a second periodic measurementsignal 11B, wherein the first periodic measurement signal 11A and thesecond periodic measurement signal 11B have a standard period length,and wherein a phase of the second periodic measurement signal 11B isshifted with respect to a phase of the first periodic measurement signal11A. This makes it possible to assign a combination of a measurementsignal value of the first periodic measurement signal 11A and ameasurement signal value of the second periodic measurement signal 11Bto an unambiguous angular position of the magnetic ring 21 or of theshaft 22, for example. In examples, the first periodic measurementsignal 11A and the second periodic measurement signal 11B are each basedon a magnetic field component which is perpendicular to the respectiveother magnetic field component. As a result, the first periodicmeasurement signal and the second periodic measurement signal may bephase-shifted through 90° with respect to one another. The angularposition can therefore be determined using an arc tangent function, forexample. In the design of the magnetic ring as a diametrically polarizedmagnetic ring with a pole pair, as shown in FIG. 2A, this way ofdetermining the angular position may be unambiguous.

In examples, determination of an item of position information or of arotational angle using an arc tangent function may be implemented usingan atan2 function.

Like in the example schematically illustrated in FIG. 2B, the magneticring 21 may also have a plurality of pole pairs, for example three polepairs. A number of periods of the at least one periodic measurementsignal 11A; 11B, which are generated by the position sensor 60 during acomplete revolution of the magnetic field transducer 20, may beproportional to a number of the pole pairs, for example. A higher numberof pole pairs may be advantageous for a degree of accuracy with whichthe position information 19 is determined.

In examples, the processing unit 15 is designed to use a previous itemof position information to determine the position information 19 usingthe respective assigned calibration function. The previous positioninformation may be, for example, the last item of position informationwhich is known to the processing unit 15 and relates to the position ofthe magnetic field transducer relative to the position sensor and wasdetermined at a previous time. For example, the processing unit 15 maybe designed to select that solution from a plurality of possiblesolutions of the calibration function which is closest to the previousposition information as the position information 19 or as the estimatedvalue for the position information 19. On account of the use of theprevious position information, the processing unit 15 may be able tounambiguously determine the position information 19 on the basis of anindividual measurement signal of the at least one periodic measurementsignal.

In examples, the processing unit 15 is designed to use the positioninformation determined last as the previous position information afterthe apparatus 10 has been switched on. The position informationdetermined last may have been determined, for example, at an earliertime using a calibration function, for example in the period sinceswitch-on. On account of the use of the position information determinedlast as the previous position information, the assumption that adifference between the current position and the position at the time ofdetermining the previous position is small can apply with a high degreeof probability, as a result of which a correct selection of the positioninformation 19 can be ensured.

In examples, the processing unit 15 is designed to determine theprevious position information on the basis of a first measurement signalvalue of the first periodic measurement signal 11A and on the basis of asecond measurement signal value of the second periodic measurementsignal 11B using an arc tangent function when the apparatus is switchedon. Alternatively, the processing unit 15 can also be designed todetermine the previous position information on the basis of a firstmeasurement signal value of the first periodic measurement signal 11Aand on the basis of a second measurement signal value of the secondperiodic measurement signal 11B using another combination of the firstmeasurement signal value and the second measurement signal value whichis based on trigonometric relationships when the apparatus is switchedon. During switch-on, no calibration function determined at an earliertime using one of the assigned calibration functions is available, forexample, or this earlier position information is inaccurate, for examplebecause the position changed while the apparatus 10 was switched off.Determination of the previous position information using the arc tangentfunction or using the other combination of the first measurement signalvalue and of the second measurement signal value may then be a goodapproximation for the previous position information and can therefore beused as a good starting value for iteratively adapting an estimatedvalue for the position information.

In examples, the apparatus 10 has a calibration unit 14, wherein thecalibration unit 14 is designed to determine the Fourier coefficients ofthe respective assigned calibration function on the basis of therespective multiplicity of measurement signal values of the respectiveperiodic measurement signals. The respective multiplicity of measurementsignal values may comprise, for example, measurement signal values fromone or more periods of the respective periodic measurement signal. Sincethe apparatus 10 has the calibration unit 14, the apparatus 10 may beable to independently newly determine the respective calibrationfunction, for example without being dependent on a calculation ordetermination by an external calibration unit 14.

In examples, the Fourier series has the form

$\begin{matrix}{{{{\overset{\sim}{X}\lbrack n\rbrack} = {\sum_{k = 0}^{N - 1}{c_{k}*e^{j\frac{2\pi}{N}kn}}}};{c_{k} = {\frac{1}{N}{\sum_{n = 0}^{N - 1}{{\overset{\sim}{x}\lbrack n\rbrack}*e^{{- j}\frac{2\pi}{N}kn}}}}}},} & (1)\end{matrix}$

wherein {tilde over (X)} represents, for example, a measurement signalvalue of a periodic measurement signal, n represents a phase of theperiodic measurement signal which is intended to be assigned to therotational angle θ for example, and c_(k) represents, for example, ak-th order Fourier coefficient. A summand of the zeroth order (forexample for k=0) of the Fourier series may represent, for example, aconstant term, that is to say a term independent of the phase. A summandof the k-th order, with k>0, can then represent a term which, inexamples, can be represented in a simplified manner as a sine or cosinefunction of k times the phase.

In examples, the first assigned calibration function can represent thefirst periodic measurement signal using a Fourier series of Fouriercoefficients c_(x1), c_(x2), c_(x3) which differ from zero, and can beexpressed in a simplified manner, for example, as:

X=c _(X1)*cos(θ+φ_(x1))+c _(x2)*cos(2*θ+φ_(x2))+c_(X3)*cos(3*θ+φ_(x3))+O _(x)   (2)

In this example, X denotes a value of the first assigned calibrationfunction at the position θ. O_(X) may be an offset or a constant offsetfor the value of the calibration function. φ_(x1), φ_(x2), φ_(x3) mayeach be a phase offset for the respective summands of the calibrationfunction and may be constants which are determined together with theFourier coefficients during calibration, for example.

For example, the second assigned calibration function can accordinglyrepresent the second periodic measurement signal using a Fourier seriesof Fourier coefficients c_(y1), c_(y2), c_(y3) which differ from zero,and can be expressed in a simplified manner, for example, as:

Y=c _(y1)*sin(θ+φ_(y1))+c _(y2)*sin(2*θ+φ_(y2))+c_(y3)*sin(3*θ+φ_(y3))+O _(y)   (3)

In this case, Y can denote the value of the second assigned calibrationfunction.

In examples, the calibration unit 14 is designed to determine theFourier coefficients of the respective assigned calibration functionusing a discrete Fourier analysis or a DFT analysis (DFT=DiscreteFourier Transformation). A Fourier analysis is a very efficient and fastmethod for determining the Fourier coefficients.

In examples, the calibration unit 14 is designed to also determine theFourier coefficients of the respective assigned calibration function onthe basis of a multiplicity of reference position values, wherein areference position value is respectively assigned to a measurementsignal value of the multiplicity of measurement signal values of one ormore of the at least one periodic measurement signal. For example, thecalibration unit is designed to assign a respective measurement signalvalue of the respective multiplicity of measurement signal values to areference position value in order to obtain a multiplicity of valuepairs assigned to the respective periodic measurement signal and todetermine the respective assigned calibration function on the basis ofthe respective multiplicity of value pairs. The calibration function canbe determined in a particularly accurate manner with the aid of thereference position values.

In examples, the calibration unit 14 is designed to determine themultiplicity of reference position values on the basis of an item ofinformation relating to a speed of the relative movement and on thebasis of an evaluation of a period length of the at least one periodicmeasurement signal. For example, the calibration unit 14 may be designedto assign a reference position value to a measurement signal value ofthe respective multiplicity of measurement signal values assuming aconstant speed of the relative movement and assuming that the individualmeasurement signal values of the respective multiplicity of measurementsignal values are recorded at equal intervals. For example, thecalibration unit 14 may be designed to determine the multiplicity ofreference position values independently or itself in order and to carryout a self-calibration on the basis thereof. As a result, the apparatusmay be able to determine the respective assigned calibration functionindependently, that is to say without an additional apparatus forexample, even during operation. The apparatus may therefore ensurepermanently precise determination of the position information.

In examples, the calibration unit 14 is designed to determine themultiplicity of reference position values using an item of referenceposition information provided by a decoder, for example a positiondecoder or a decoder of a stepping motor, wherein the decoder isdesigned to determine the reference position information on the basis ofthe relative movement. For example, the apparatus 10 may be designed toreceive the multiplicity of reference values from the decoder. Referenceposition values provided by a decoder can be particularly accurate andcan therefore make it possible to precisely determine the calibrationfunction.

In examples, the respective assigned calibration function comprises theFourier series in a representation simplified using trigonometricmethods. The simplified representation of the Fourier series makes itpossible, for example, to reduce a number of function calls used tocalculate the respective value of the respective assigned calibrationfunctions at the position of the respective estimated value, with theresult that this calculation can be carried out in a particularlyefficient manner.

For example, the examples of the calibration functions X and Y(equations (2) and (3)) shown above can be simplified or optimized usingthe equations

sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

cos(A+B)=cos(A)*sin(B)−sin(A)*cos(B)

sin(2x)=2*sin(x)*cos(x)

cos(2x)=cos² x−sin² x

A range of calculations, for example codec calculations, for example anumber of function calls, can therefore be reduced.

In examples, the processing unit 15 is designed to iteratively adapt arespective estimated value, for example an estimated value for theposition information, for example a rotational angle θ, on the basis ofthe previous position information in order to reduce a distance betweenthe respective measurement signal value and a respective value of therespective assigned calibration functions at the position of therespective estimated value and to determine the position information 19on the basis of the respective estimated value. For example, theprocessing unit 15 is designed to iteratively adapt a first estimatedvalue on the basis of the previous position information in order toreduce a distance between the first measurement signal value and a valueof the first assigned calibration functions at the position of the firstestimated value and to determine the position information 19 on thebasis of the first estimated value. In addition, the processing unit 15may be designed to accordingly determine the position information on thebasis of a further estimated value using the further calibrationfunction. For example, the distance between the respective measurementsignal value and the respective value of the respective assignedcalibration functions at the position of the respective estimated valueis iteratively reduced until it undershoots a maximum deviation.Suitably choosing the maximum deviation makes it possible, for example,to set a compromise between a speed or a computing complexity of theadaptation and an accuracy of the result in an application-specificmanner. Since the respective estimated value is adapted on the basis ofthe previous position information, a number of iteration steps is keptlow. As a result, it is possible to determine the position information19 quickly and with little computing complexity and it can also beensured that a periodic measurement signal alone also results in correctdetermination of the position information 19 with a high degree ofprobability. Iterative adaptation of the respective estimated valuemakes it possible to efficiently solve the respective assignedcalibration function.

In examples, the processing unit 15 is designed to adapt the respectiveestimated value according to the Newton method or another approximationmethod. The Newton method can be used in a particularly efficient mannerto minimize the distance between the respective measurement signal valueand the respective value of the respective assigned calibrationfunctions at the position of the respective estimated value. This makesit possible to determine the position information 19 quickly and withlittle computing complexity.

In examples, the processing unit 15 is designed to iteratively adapt afirst estimated value and a second estimated value on the basis of theprevious position information 19 in order to reduce a distance betweenthe respective measurement signal value and a respective value of therespective assigned calibration functions for the respective estimatedvalue and to weight the first estimated value and the second estimatedvalue for determining the position information 19. For example, theprocessing unit 15 is designed to calculate a weighted average of thefirst estimated value and of the second estimated value in order todetermine the position information 19. Weighting the first and secondestimated values results in a combination of the first periodicmeasurement signal and the second periodic measurement signal fordetermining the position information 19, as a result of which it ispossible to compensate for any possible inaccuracy of the first assignedcalibration function and of the second assigned calibration function.The first estimated value and the second estimated value are combined ina particularly favorable manner by the weighting. For example, theprocessing unit 15 is designed to give a more inaccurate estimated valuea lower weighting than a more accurate estimated value, as a result ofwhich the position information 19 can be determined in a very accuratemanner. The weighting of the first estimated value and of the secondestimated value is particularly effective if the first periodicmeasurement signal and the second periodic measurement signal arephase-shifted through approximately 90° with respect to one anothersince, in this case, one estimated value is particularly accurate atprecisely those positions at which the respective other estimated valueis particularly inaccurate.

In examples, the processing unit 15 is designed to weight the firstestimated value and the second estimated value on the basis of arespective gradient of the respective assigned calibration function atthe position of the respective estimated value, wherein the respectiveweighting is greater, the greater the respective gradient. For example,the processing unit 15 is designed to weight the respective estimatedvalues using a respective weighting function 51A, 51B, wherein therespective weighting function 51A, 51B describes the contributions ofthe respective estimated values to the position information 19 in aposition-dependent manner, and wherein the contributions of therespective estimated value are greater, the greater the respectivegradient of the respective calibration function at the correspondingposition. Such weighting can ensure that a very high degree of accuracyof the position information 19 is achieved despite a small number ofiteration steps when adapting the estimated values.

FIG. 5 shows a graph having examples of a first weighting function 51Aof the first periodic measurement signal 11A and of a second weightingfunction 51B of the second periodic measurement signal 11B on the basisof the rotational angle θ. The weighting functions shown in FIG. 5 aresuitable, for example, for weighting the examples of periodicmeasurement signals 11A, 11B shown in FIG. 3.

Examples of this disclosure provide a position sensor 60, wherein theposition sensor 60 has a measurement unit which is designed to generateat least one periodic measurement signal when a magnetic fieldtransducer 20 moves relative to the position sensor 60, and wherein theposition sensor has an apparatus 10 for determining an item of positioninformation 19 order to determine the position information 19 on thebasis of the at least one periodic measurement signal.

In examples, the measurement unit has a magnetic field sensor, forexample an xMR sensor or a Hall sensor. As a result of the combinationof an xMR sensor with the apparatus 10, the position sensor can beproduced efficiently, for example using semiconductor manufacturingprocesses, and may be able to determine the position information 19 witha high degree of accuracy.

In examples, the position sensor 60 has an integrated circuit, whereinthe integrated circuit comprises the measurement unit and the apparatus10 for determining an item of position information 19. For example, themeasurement unit and the apparatus 10 are arranged on a commonsubstrate. As a result of the fact that the integrated circuit comprisesboth the measurement unit and the apparatus 10, the position sensor canbe designed in a particularly space-saving saving manner, can beproduced in a particularly simple manner and can be arrangedparticularly easily in a circuit, for example on a printed circuit board(PCB).

In examples, a first integrated circuit comprises the measurement unitand a second integrated circuit comprises the apparatus 10 fordetermining an item of position information 19. For example, the secondintegrated circuit is designed to enable a high computing power of theapparatus 10. As a result of the separate circuits, the measurement unitand the apparatus 10 can be produced, for example, separately, forexample using manufacturing processes of different complexity, thusmaking it possible to save costs.

FIG. 7 shows a schematic illustration of an example of an arrangement ofa position sensor 60 and a magnetic field transducer 20, wherein theposition sensor 60 has a measurement unit 61.

In examples, the magnetic field transducer 20 has a magnetic ring 21which is arranged around an axis of rotation and has magnetic poleswhich alternate in the radial direction, wherein the measurement unithas a magnetic field sensor which is stationary with respect to arotation of the magnetic ring around the axis of rotation.

FIG. 8 shows a method 800 for determining an item of positioninformation 19 relating to a position of a magnetic field transducer 20relative to a position sensor 60, wherein the position sensor 60 isdesigned to generate at least one periodic measurement signal when themagnetic field transducer 20 moves relative to the position sensor 60.The method 800 comprises determining 810 the Fourier coefficients on thebasis of a respective multiplicity of measurement signal values of therespective periodic measurement signal. The method 800 also comprisesdetermining 820 the position information 19 on the basis of a respectivemeasurement signal value of a respective periodic measurement signalusing a calibration function assigned to the respective periodicmeasurement signal, wherein the assigned calibration function representsthe respective periodic measurement signal using a Fourier series havinga respective plurality of Fourier coefficients which differ from zeroand are of an order greater than zero. The determination 820 of theposition information 19 comprises at least approximately solving theassigned calibration function for the respective measurement signalvalue.

The illustrated sequence of method steps should be understood by way ofexample. The steps can also be carried out in a different order, at thesame time or individually. The individual steps can be carried out, inparticular, with a different frequency; for example, the determination820 of the position information 19 can be carried out more often thanthe determination 810 of the Fourier coefficients.

In examples, this disclosure relates to a method for calibrating andcompensating for signals from sensors, for example in “out-of-shaft”,“end-of-shaft” or “integrated end-of-shaft” sensor systems. FIG. 9 showsa flowchart of an example of a method 900 for calibrating andcompensating for such signals. The method 900 is based on the method800. The method 900 comprises a calibration 910 which is based on thedetermination 810 of the Fourier coefficients, for example. Thecalibration can be carried out once (one-off calibration), normally atthe end of the production of a module for determining the positioninformation 19 outside the shaft, or continuously or periodically in use(self-calibration). The calibration 910 comprises collecting 911 aplurality of ADC values, for example recording the multiplicity ofmeasurement signal values of the periodic measurement signal, using anxMR sensor or a sensor based on the Hall effect, for example using themeasurement unit 61. The calibration also comprises calculating 912optimal signal coefficients or estimating parameters, for example theFourier coefficients, using DFT algorithms. In addition, the correctreference angles should be used for these ADC values. For a one-offcalibration, these values can be determined using a dedicated rotaryencoder or can be derived from the known angular positions of a steppingmotor. For a self-calibration, an equidistant sampling rate and anapproximately constant angular velocity can be assumed (this is alsopossible for a one-off calibration). The validity of these assumptionscan be checked by observing the periods of a plurality of revolutions.Finally, the calibration comprises estimating an optimal set ofparameters, for example Fourier coefficients and phase shifts. Themethod 900 also comprises a compensation 920 which is based on thedetermination 820 of the position information 19, for example. Thecompensation 920 comprises correcting recorded sensor results ormeasurement values, for example a measurement signal value, and finallycalculating the estimated mechanical angle 0, for example the positioninformation 19. During switching-on, for example the switching-on of theapparatus 10, a first angle, for example the previous positioninformation 19, may be calculated 930 using an arc tangent function or asignal analysis. In contrast to sensor applications at the end of ashaft, the magnetic amplitudes Ax and Ay of the cosine and sinecomponents of the magnetic field, as shown in FIG. 2A, generally differin sensor applications outside a shaft. The signals are greatly deformedover 360°. Such a deformation can be seen in FIG. 3 where raw signalvalues from both channels of a GMR sensor with a vertical orientation(air gap 26=1.6 mm, z offset 28=1 mm, offset in the y direction=0.4 mm(directions based on FIG. 2A)) are shown. Ideal cosine and sinefunctions are additionally shown there as an orientation aid. The rawsignal values, for example as shown in FIG. 3, for example themultiplicity of measurement signal values, can be broken down into aFourier series according to equation (1) and can be written as anextracted and simplified Fourier series for three coefficients accordingto equations (2) and (3). A DFT analysis of the channels makes itpossible to determine c_(x1), c_(x2), φ_(x1), φ_(x2), φ_(x3), φ_(y1),c_(y2), c_(y3), φ_(y1), φ_(y2), φ_(y3). For example, c₁ shows thegreatest influence, followed by c₃ and c₂. The number of coefficientscan be increased or reduced in any desired manner. FIGS. 4A-C show theinfluence of a different set of coefficients on the curve adaptation(dashed lines) to raw signal values (solid lines). For example, nosignificant improvement can arise in the case of more than threecoefficients and the residual error of the angle may be almost as largeas in current solutions in the case of only one coefficient, cf. FIG.4A. Two or three coefficients are therefore advantageous, for example.New ADC values, for example measurement signal values, are recordedduring operation. The mechanical angle, for example the positioninformation 19, is determined by varying an estimated angle θ′, forexample an estimated value, for example one estimated value for arespective periodic measurement signal or for each channel in each case,for example θ_(x)′ and θ_(y)′, in such a manner that the Fourier series,for example the respective assigned calibration function,

X′=c _(x1)*cos(θ_(x)′+φ_(x1))+c _(x2)*cos(2*θ_(x)′+φ_(x2))+c_(x3)*cos(3*θ_(x)′+φ_(x3))+O _(x)

Y′=c _(y1)*cos(θ_(y)′+φ_(y1))+c _(y2)*cos(2*θ_(y)′+φ_(y2))+c_(y3)*cos(3*θ_(y)′+φ_(y3))+O _(y)

for example a value X′ or Y′ of the respective assigned calibrationfunction, meets the conditions

min (|X−X′|), min (|Y−Y′|),

wherein X and Y are, for example, measured ADC values of the twochannels, for example respective measurement signal values of therespective periodic measurement signal. On account of a high degree ofinaccuracy of the method at positions at which the signal has a minimumor a maximum, the mechanical angle θ′ should be calculated using aweighted average of both channels. Examples of weighting functions 51A,51B for the X channel 11A and the Y channel 11B are shown in FIG. 5. Themaximum for a value is at the position at which the signal exhibits thegreatest change. The weighting functions 51A, 51B can be described, forexample, using the following equation:

$\theta = \frac{{\theta_{x}^{\prime}*\left( {1 - {{\cos \left( {\theta_{x}^{\prime} + \phi_{x}} \right)}}} \right)} + {\theta_{y}^{\prime}*\left( {1 - {{\sin \left( {\theta_{y}^{\prime} + \phi_{y}} \right)}}} \right)}}{\left( {1 - {{\cos \left( {\theta_{x}^{\prime} + \phi_{x}} \right)}^{2}}} \right) + \left( {1 - {{\sin \left( {\theta_{y}^{\prime} + \phi_{y}} \right)}^{2}}} \right)}$

That angle θ calculated in this manner can then be used as the startingvalue, for example as the previous position information 19, for the nextADC value, for example for determining the next item of positioninformation 19.

FIGS. 10A-B show an example of a comparison of the evaluated angle, forexample the determined position information 19, with a reference system,for example a current solution. The residual error Δθ of the rotationalangle for a sensor with a vertical orientation (Ag=1.6 mm, z offset 28=1mm, offset in the y direction=0.4 mm (directions based on FIG. 2A)) fora current compensation (FIG. 10A) and the approximation process or thedisclosed compensation 820, 920 (FIG. 10B) is shown. The residual errorof the rotational angle can be drastically reduced using the lattermethod in comparison with current methods. FIGS. 6A and 6B show maximumangle errors 60, for example maximum residual errors of the rotationalangle, plotted against the z offset 28 for sensor arrangements of a GMRsensor with different air gaps 26 for current compensation methods, cf.FIG. 6A, and the disclosed method 900, cf. FIG. 6B. FIGS. 6A-B showexamples of the effectiveness of differently sized air gaps Ag anddistances z between the magnet and the sensor of the disclosed methodusing three coefficients, for example Fourier coefficients. The maximumerror can be reduced, for example, from 4.5° (Ag=1.6 mm, z=1.4 mm) tobelow 1°, which may be sufficiently good for many applications, and evenbelow 0.5° is possible. With only two coefficients, the angle error maybe around 1° and, with only one coefficient, it may be at the level ofstandard compensation. The disclosed method can significantly reduce theresidual error of the determined rotational angle in sensor arrangementsoutside the shaft and is able to compensate for a mechanical shiftduring the production process.

In examples, different possibilities can be used to integrate thedisclosed apparatus in a sensor component. For example, the apparatuscan be implemented with the sensor as one component, for example usingintegration on a silicon wafer, that is to say the apparatus uses thesame technology as the sensor. Alternatively, the disclosed apparatusand the sensor can be implemented in two component parts, with theresult that the calculations are carried out in a second component. Thismakes it possible to produce the sensor using one technology and toproduce the component part for calculations using another technology.

In examples, the disclosed method for compensating for or determining anitem of position information 19 can be carried out in a sensor or in anexternal microcontroller, for example a microcontroller separate fromthe sensor.

In examples, the disclosure relates to a calibration and determinationof optimum compensation parameters and algorithms for sensorarrangements outside a shaft. As such, they can be directly used by auser, for example, during or after the production of the sensor module

In examples, the position sensor 60 has a Hall sensor and the apparatus10 is designed to normalize the at least one periodic measurement signalin order to obtain the position information 19 in normalized form on thebasis of a respective measurement signal value of a respective periodicmeasurement signal.

In examples of the present disclosure, the processing circuit can beimplemented using any desired suitable circuit structures, for examplemicroprocessor circuits, ASIC circuits, CMOS circuits and the like. Inexamples, the processing circuit may be implemented as a combination ofhardware structures and machine-readable instructions. For example, theprocessing circuit may have a processor and storage devices which storemachine-readable instructions which result in the performance of methodsdescribed herein when they are executed by the processor.

Although some aspects of the present disclosure have been described asfeatures in connection with an apparatus, it is clear that such adescription can likewise be considered to be a description ofcorresponding method features. Although some aspects have been describedas features in connection with a method, it is clear that such adescription can also be considered to be a description of correspondingfeatures of an apparatus or of the functionality of an apparatus.

Some or all of the method steps can be carried out by a hardwareapparatus (or using a hardware apparatus), for example a microprocessor,a programmable computer or an electronic circuit. In some exampleimplementations, some or a plurality of the most important method stepscan be carried out using such an apparatus.

Depending on particular implementation requirements, exampleimplementations of the disclosure can be implemented in hardware orsoftware or at least partially in hardware or at least partially insoftware. The implementation can be carried out using a digital storagemedium, for example a floppy disk, a DVD, a Blu-ray disc, a CD, a ROM, aPROM, an EPROM, an EEPROM or a flash memory, a hard disk or anothermagnetic or optical memory which stores electronically readable controlsignals which interact or can interact with a programmable computersystem in such a manner that the respective method is carried out.Therefore, the digital storage medium may be computer-readable.

Some example implementations according to the disclosure thereforecomprise a data carrier having electronically readable control signalswhich are able to interact with a programmable computer system in such amanner that one of the methods described herein is carried out.

Example implementations of the present disclosure can generally beimplemented as a computer program product having a program code, whereinthe program code is effective to carry out one of the methods when thecomputer program product runs on a computer.

The program code may be stored on a machine-readable carrier, forexample.

Other example implementations comprise the computer program for carryingout one of the methods described herein, wherein the computer program isstored on a machine-readable carrier. In other words, an exampleimplementation of the disclosed method is therefore a computer programhaving a program code for carrying out one of the methods describedherein when the computer program runs on a computer.

A further example implementation of the disclosed methods is therefore adata carrier (or a digital storage medium or a computer-readable medium)on which the computer program for carrying out one of the methodsdescribed herein is recorded. The data carrier or the digital storagemedium or the computer-readable medium is typically tangible and/ornon-volatile.

A further example implementation of the disclosed method is therefore adata stream or a sequence of signals representing the computer programfor carrying out one of the methods described herein. The data stream orthe sequence of signals may be configured, for example, to betransferred via a data communication connection, for example via theInternet.

A further example implementation comprises a processing device, forexample a computer or a programmable logic component, which isconfigured or adapted to carry out one of the methods described herein.

A further example implementation comprises a computer on which thecomputer program for carrying out one of the methods described herein isinstalled.

A further example implementation according to the disclosure comprisesan apparatus or a system which is designed to transmit a computerprogram for carrying out at least one of the methods described herein toa receiver. The transmission can be carried out electronically oroptically, for example. The receiver may be, for example, a computer, amobile device, a storage device or a similar apparatus. The apparatus orthe system may comprise, for example, a file server for transmitting thecomputer program to the receiver.

In some example implementations, a programmable logic component (forexample a field programmable gate array, FPGA) can be used to carry outsome or all of the functionalities of the methods described herein. Insome example implementations, a field programmable gate array caninteract with a microprocessor in order to carry out one of the methodsdescribed herein. The methods are generally carried out in some exampleimplementations by any desired hardware apparatus. This may beuniversally usable hardware such as a computer processor (CPU) orhardware specific to the method, for example an ASIC.

The preceding disclosure provides illustrations and descriptions, butthe intention is not for the disclosure to be exhaustive or for theimplementations to be restricted to the precise form disclosed.Modifications and variations are possible with regard to the abovedisclosure or can be obtained from the practice of the implementations.Although certain combinations of features are cited in the patent claimsand/or disclosed in the description, there is no intention for thesefeatures to restrict the disclosure of possible implementations. Infact, numerous ones of these features can be combined in ways which arenot specifically cited in the patent claims and/or disclosed in thedescription. Although any of the dependent patent claims cited belowpossibly depends directly only on one or a number of patent claims, thedisclosure of possible implementations comprises any dependent patentclaim in combination with all other patent claims in the set of patentclaims.

The examples described above are only representative of the principlesof the present disclosure. It should be understood that modificationsand variations of the arrangements and details described are obvious toexperts. The intention is therefore for the disclosure to be limitedonly by the accompanying patent claims and not by the specific detailswhich are stated for the purpose of describing and explaining theexamples.

LIST OF REFERENCE SIGNS

10 Apparatus for determining an item of position information

11A First periodic measurement signal

11B Second periodic measurement signal

13A First assigned calibration function

15 Processing unit

19 Position information

20 Magnetic field transducer

21 Magnetic ring

22 Shaft

24 Axis of rotation

26 Thickness of the air gap

28 z offset

51A First weighting function

51B Second weighting function

60 Position sensor

61 Measurement unit

800 Method for determining an item of position information

810 Determination of the Fourier coefficients

820 Determination of the position information

900 Method for determining an item of position information

910 Calibration

911 Collection of a plurality of ADC values

912 Calculation of optimum signal coefficients

920 Compensation

921 Collection of a set of ADC values

922 Estimation of the angle

930 Calculation of the angle during switching-on

1. An apparatus comprising: a processing unit to: determine an item ofposition information relating to a position of a magnetic fieldtransducer relative to a position sensor, wherein the position sensor isconfigured to generate at least one periodic measurement signal when themagnetic field transducer moves relative to the position sensor, whereinthe position information is determined based on a respective measurementsignal value of a respective periodic measurement signal using acalibration function assigned to the respective periodic measurementsignal, wherein the assigned calibration function represents therespective periodic measurement signal using a Fourier series having arespective plurality of Fourier coefficients which differ from zero andare of an order greater than zero, wherein the Fourier coefficients aredetermined based on a respective multiplicity of measurement signalvalues of the respective periodic measurement signal, and wherein theprocessing unit is configured to at least approximately solve theassigned calibration function for the respective measurement signalvalue in order to determine the position information.
 2. The apparatusas claimed in claim 1, wherein the processing unit is configured to usea previous item of position information to determine the positioninformation using the respective assigned calibration function.
 3. Theapparatus as claimed in claim 2, wherein the processing unit isconfigured designed to iteratively adapt a respective estimated valuebased on the previous position information in order to reduce a distancebetween the respective measurement signal value and a respective valueof the respective assigned calibration functions at the position of therespective estimated value and to determine the position informationbased on the respective estimated value.
 4. The apparatus as claimed inclaim 3, wherein the processing unit is configured to adapt therespective estimated value according to a Newton method or anotherapproximation method.
 5. The apparatus as claimed in claim 1, whereinthe respective assigned calibration function comprises the Fourierseries in a representation simplified using trigonometric methods. 6.The apparatus as claimed in claim 1, wherein the at least one periodicmeasurement signal comprises a first periodic measurement signal and asecond periodic measurement signal, wherein the first periodicmeasurement signal and the second periodic measurement signal have astandard period length, and wherein a phase of the second periodicmeasurement signal is shifted with respect to a phase of the firstperiodic measurement signal.
 7. The apparatus as claimed in claim 6,wherein the processing unit is configured to: iteratively adapt a firstestimated value and a second estimated value based on previous positioninformation in order to reduce a distance between the respectivemeasurement signal value and a respective value of the respectiveassigned calibration functions for the respective estimated value, andweight the first estimated value and the second estimated value in orderto determine the position information.
 8. The apparatus as claimed inclaim 7, wherein the processing unit is configured to weight the firstestimated value and the second estimated value based on a respectivegradient of the respective assigned calibration function at the positionof the respective estimated value, wherein the respective weighting isgreater, the greater the respective gradient.
 9. The apparatus asclaimed in claim 7, wherein the processing unit is configured todetermine the previous position information based on a first measurementsignal value of the first periodic measurement signal and based on of asecond measurement signal value of the second periodic measurementsignal using an arc tangent function when the apparatus is switched on.10. The apparatus as claimed in claim 9, wherein the processing unit isconfigured to use the position information determined last as theprevious position information after the apparatus has been switched on.11. The apparatus as claimed in claim 1, further comprising: acalibration unit (H), wherein the calibration unit (H) is configured todetermine the Fourier coefficients of the respective assignedcalibration function based on the respective multiplicity of measurementsignal values of the respective periodic measurement signals.
 12. Theapparatus as claimed in claim 11, wherein the calibration unit isconfigured to also determine the Fourier coefficients of the respectiveassigned calibration function based on of a multiplicity of referenceposition values, wherein a reference position value is respectivelyassigned to a measurement signal value of the multiplicity ofmeasurement signal values of one or more of the at least one periodicmeasurement signal.
 13. The apparatus as claimed in claim 12, whereinthe calibration unit is configured to determine the multiplicity ofreference position values based on of an item of information relating toa speed of a relative movement and based on an evaluation of a periodlength of the at least one periodic measurement signal.
 14. Theapparatus as claimed in claim 12, wherein the calibration unit isconfigured to determine the multiplicity of reference position valuesusing an item of reference position information provided by a decoder,wherein the decoder is configured to determine the reference positioninformation based on a relative movement.
 15. The apparatus as claimedin claim 11, wherein the calibration unit is configured to determine theFourier coefficients of the respective assigned calibration functionusing a discrete Fourier analysis.
 16. A position sensor comprising: ameasurement unit configured to generate at least one periodicmeasurement signal when a magnetic field transducer moves relative tothe position sensor, and an apparatus for determining an item ofposition information as claimed in claim 1 in order to determine theposition information based on the at least one periodic measurementsignal.
 17. The position sensor as claimed in claim 16, wherein theposition sensor has an integrated circuit, and wherein the integratedcircuit comprises the measurement unit and the apparatus for determiningan item of position information.
 18. The position sensor as claimed inclaim 16, wherein a first integrated circuit comprises the measurementunit, and wherein a second integrated circuit comprises the apparatusfor determining an item of position information.
 19. The position sensoras claimed in claim 16, wherein the magnetic field transducer has amagnetic ring which is arranged around an axis of rotation and hasmagnetic poles which alternate in a radial direction, and wherein themeasurement unit has a magnetic field sensor which is stationary withrespect to a rotation of the magnetic ring around the axis of rotation.20. A method for determining an item of position information relating toa position of a magnetic field transducer relative to a position sensor,wherein the position sensor is configured to generate at least oneperiodic measurement signal when the magnetic field transducer movesrelative to the position sensor, wherein the method comprises:determining the position information based on a respective measurementsignal value of a respective periodic measurement signal using acalibration function assigned to the respective periodic measurementsignal, wherein the assigned calibration function represents therespective periodic measurement signal using a Fourier series having arespective plurality of Fourier coefficients which differ from zero andare of an order greater than zero, wherein the determination of theposition information comprises at least approximately solving theassigned calibration function for the respective measurement signalvalue, and determining the Fourier coefficients based on a respectivemultiplicity of measurement signal values of the respective periodicmeasurement signal.
 21. A computer program having a program code forcarrying out the method as claimed in claim 20 when the program runs ona computer.